MATLAB Implementation of Cubic Spline Interpolation

Below is a MATLAB program for cubic spline interpolation. Follow these steps to implement and execute the code:

1. Launch MATLAB software on your system.

2. Navigate to the "File" menu and select "New" to create a new script.

3. Input the following implementation code in the editor window:

% Define input data points (modify these with your actual data)

x = [0, 1, 2, 3, 4];

y = [0, 1, 0, 1, 0];

% Generate interpolation points using cubic spline algorithm

% The spline() function implements piecewise cubic polynomial interpolation

% that ensures continuous first and second derivatives at knot points

xx = linspace(0, 4, 101);

yy = spline(x, y, xx);

% Visualize original data and interpolated curve

% 'o' markers show original points, line shows smooth spline interpolation

plot(x, y, 'o', xx, yy);

4. Save the file through the "File" menu > "Save" option to your local directory.

This program now enables cubic spline interpolation computation and visualization. Remember to substitute the x and y arrays with your actual dataset. The algorithm automatically handles boundary conditions and creates a smooth curve that passes through all given data points while maintaining C² continuity.